Mathematical and Physical Journal
for High Schools
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Problem A. 558. (March 2012)

A. 558. Prove that there exists a constant C>0 for which the following statement holds: if n is a positive integer and A_1,A_2,\ldots,A_N\subset\{1,2,\ldots,n\} are sets such that every two of them has at least two, and every three of them has at most three elements in common, then N<Cn2.

(Proposed by: Z. Gyenes, Budapest)

(5 pont)

Deadline expired on April 10, 2012.


2 students sent a solution.
5 points:Ágoston Tamás, Janzer Olivér.

Problems in Mathematics of KöMaL, March 2012